"[T]hats why we move into the abstract world of ideas, where things behave the way that we want them to... [T]hat can be a scary move... because... in the real world you get to touch things... throw things... Whereas in the abstract world... if the logic doesnt do the thing that you want... Theres nothing you can do about it. Thats just how it works... [T]he upside... is that if you align yourself with the way logic is supposed to work, then everything behaves the way you want it to, because everything behaves perfectly logically... [I]t is the only place where everything behaves perfectly logically."
Eugenia Loh-Gene Cheng is a British mathematician, educator and concert pianist. Her mathematical interests include higher category theory, and as a pianist she specialises in lieder and art song. She is also known for explaining mathematics to non-mathematicians to combat math phobia, often using analogies with food and baking. Cheng is a scientist-in-residence at the School of the Art Institute
"All our dreams can come true as long as we have the right dreams... [A]s long as we think logically, this is the world where everything behaves correctly, and... where any toy we want, we can play with, as soon as weve dreamed it up."
"We can go through life, and this is why people do believe they can go through life without needing to know any maths... [S]o when... we go "Math is really important!" They can just go, "Well, I dont... do any of those things, and Im just fine." ...Yeah, you can be just fine, but wouldnt you like to be better?"
"I am going to show that mathematics... is precisely "that which is easy.""
"... I wish we could educate people not just to be able to do things and know things, but to be nicer humans — and to get their self-esteem not from being better at something than someone else — but from how much they are able to help someone else do something."
"[S]omething is easy if it is attainable by logical thought processes.... without having to resort to imagination, guesswork, luck, gut feeling, convoluted interpretation, leaps of faith... drugs, violence... [etc.]"
"[I]n order to study anything logically, we have to ignore all the pesky details that prevent it from behaving logically, and... move into the idealized world... rather than the real world of things... [T]his... is what... abstraction... is..."